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" AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. "
The New Practical Builder and Workman's Companion, Containing a Full Display ... - Page 15
by Peter Nicholson - 1823 - 596 pages
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An introduction to geometry, consisting of Euclid's Elements, book ..., Volume 1

Euclides - 1884 - 182 pages
...people in general have in their minds. AXIOMS 1 — 7, 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals,...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884 - 434 pages
...Euclid's part, are never adhered to in practice.] AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the sums are equal. 3. If equals be taken from equals, the remainders aro equal. 12 EUCLID'S ELEMENTS....
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Bizarre; Notes and Queries; a Monthly Magazine of History, Folk ..., Volumes 3-4

1886 - 580 pages
...equal to each other 2. If equals be added to equals, the sums will be equal. 3. If equals be subtracted from equals, the remainders will be equal. 4. If equals be added to unequals, the sums will be unequal. 5. If equals be subtracted from unequals, the remainders will be unequal. 6....
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 420 pages
...which are equal to the same thing are equal to each other. 2. If equals be added to equals the sums will be equal. 3. If equals be taken from equals the...will be equal. 4. If equals be added to unequals the sums will be uneqtial. 5. If equals be taken from unequals the remainders will be unequal. 6. Things...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...granted the three ' demanded ' by the Postulates. AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals,...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1891 - 424 pages
...which are equal to the same thing are equal to each other. 2. If equals be added to equals the sums will be equal. 3. If equals be taken from equals the...remainders will be equal. 4. If equals be added to uuequals the sums will be unequal. 5. If equals be taken from unequals the remainders will be unequal....
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1892 - 460 pages
...been already indicated in the definitions. GENERAL AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals,...
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A Text-book of Euclid's Elements for the Use of Schools. Books I.-VI ..., Book 1

Euclid, Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...Common Notions, are known as the Axioms. GENERAL AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals,...
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A Text-book of Euclid's Elements for the Use of Schools, Book 1

Euclid - Euclid's Elements - 1904 - 488 pages
...evident that they are accepted without proof. GENERAL AXIOMS. I. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals,...
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Henley's Encyclopaedia of Practical Engineering and Allied Trades ...

1906 - 576 pages
...has based the whole of geometry on twelve axioms : — 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals the wholes are equal. 3. If equals be taken from equals the remainders are equal. 4. If equals be added to unequals...
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